Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14341
 Main Title: Interconnected systems with uncertain couplings: explicit formulae for μ-values, spectral value sets and stability radii Author(s): Karow, MichaelHinrichsen, DiederichPritchard, Anthony J. Type: Research Paper URI: https://depositonce.tu-berlin.de/handle/11303/15568http://dx.doi.org/10.14279/depositonce-14341 License: http://rightsstatements.org/vocab/InC/1.0/ Abstract: In this paper we study the variation of the spectrum of block-diagonal systems under perturbations of compatible block structure with fixed zero blocks at arbitrarily prescribed locations ("Gershgorin type perturbations''). We derive explicit and computable formulae for the associated $\mu$-values. The results are then applied to characterize spectral value sets and stability radii for such perturbed systems. By specializing our results to the scalar diagonal case the classical eigenvalue inclusion theorems of Gershgorin, Brauer and Brualdi are obtained as corollaries. Moreover it follows that the inclusion regions of Brauer and Brualdi are optimal for the corresponding perturbation structures. Subject(s): interconnected systemsspectral value setsstability radiiμ-analysisrobustness Issue Date: 11-Mar-2005 Date Available: 17-Dec-2021 Language Code: en DDC Class: 510 Mathematik MSC 2000: 93D09 Robust stability93B60 Eigenvalue problems Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin Series Number: 2005, 09 ISSN: 2197-8085 TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik Appears in Collections: Technische Universität Berlin » Publications